Diffusion is the net movement of molecules or atoms from a region of high concentration to a region of low concentration as a result of random motion of the molecules or atoms (Wikipedia).
Due to a discovery by Einstein (1905), a universal model for the random motion of microscopic particles is Brownian motion, whose mean-squared displacement increases linearly with time.
In many system with particles more complex than tiny molecules which interact with their environment (e.g. proteins, self-propelled bacteria or cells, stock market prices, …) the growth of the mean-squared displacement is no longer linear:
(Image credit Wikipedia).
The Continuous Time Random Walk (CTRW) is a model for anomalous diffusion: it can model subdiffusion with long (heavy-tailed) waiting times between steps, and superdiffusion with long (heavy-tailed) steps, and even a mixture of both.
Scientists are interested in extending the CTRW model to allow for interactions between walkers, and need tools for the computation of concentrations of random walkers. Since the beginning of the century, there has been a fruitful exchange between statistical physics, experimental physics, pure mathematics and computational mathematics, which has significantly advanced biophysics, among other fields.